Algebra

Algebra

Algebra is based of five fundamental laws, which govern the operations of addition, subtraction, multiplication, and division. Each of the laws is expressed in letters variables. Where variables a, b and c are all real numbers, any number can be substituted for a variable without conflicting with the way the rule works.

The Commutative Law of Addition: a + b = b + a. Under this law, the order in which two numbers are added has no bearing on the sum derived.

The Associative Law of Addition: a + (b + c) = (a + b) + c. Under this law, it does not matter which combination of numbers are added first, the sum remains the same.

The Commutative Law of Multiplication: ab = ba. Under this law, it does not matter which order numbers are multiplied in, the product is the same.

The Associative Law of Multiplication: a * (bc) = (ab) * c. Under this law, numbers can be multiplied in any sequence without affecting the final product.

The Distributive Law of Multiplication Over Addition: a (b + c) = ab + ac. Under this law, if a number multiplies a sum, the total is the same as the sum of the separate products of the multiplier and each of the addends represented by b and c.

The Quadratic Equation: Another key algebraic equation is the quadratic equation, in which the highest power to which the unknown quantity is raised is the second.

Algebra is the base of our civilization. Photo: Elena.

Without algebra, civilization wouldn't exist. Illustration: Megan Jorgensen.